國立高雄師範大學教學綱要(105學年度)
科目名稱：微分方程導論 ■必修 □選修 教師：李俊憲
任課班級：數學系數學組二年級
每學期開課學分數：上學期 3 學分 下學期 0 學分
總學分數： 3 學分 每週上課時數： 3 小時
連繫電話：6813 辦公地點：致理大樓608 辦公時間（Office hour）：Wed. 10:00~12:00
※※請遵守智慧財產權觀念、不得非法影印※※
一、教學目標：
- To discuss some of the properties of solutions of differential equations
- To present some of the methods that have proved effective in finding solutions, or, in some cases, approximating them.
二、教材內容：
- Introduction some basic terminology for differential equations
- The separable, linear, and exact equations
- Mathematical models for first-order equations
- Second-order linear equations
- Systems of differential equations
- Higher-order linear equations
- Laplace transforms
- Series solutions of differential equaitons
三、實施方法：講授、討論
四、評量方式：
期中考(一):30%
期中考(二):30%
期末考:40%
五、主要讀本及參考書目：
（1）主要讀本：R. Nagle, E. Saff, and A. Snider, Fundamentals of Differential Equations and Boundary Value Problem, 6th Edition, 2012.
（2）參考書目：W. Boyce and R. DiPrima, Elementry Differential Equations and Boundary Value Problems, 10th Edition, 2013.
六、教學進度：
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週 別
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內 容
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作 業
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參 考 資 料
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上
學
期
︶
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1
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Introduction (9/16彈性放假)
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Sec. 1.1-1.3
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2
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First-order equations
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Sec. 1.4, 2.2, 2.3
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3
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Sec. 2.4, 2.6
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4
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Mathematical models
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Sec. 3.2, 3.4, 4.1
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5
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Linear second-order equations (10/10放假)
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Sec. 4.2-4.4
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6
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Sec. 4.5-4.6
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7
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Midterm 1 (10/24)
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8
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Systems and phase plane analysis
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Sec. 4.7, 5.1-5.2
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9
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Sec. 5.3-5.4
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10
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Higher-order linear equations
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Sec. 5.5, 6.1
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11
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Laplace transforms
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Sec. 6.2-6.4
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12
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Sec. 7.2-7.4
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13
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Midterm 2 (12/5)
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14
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Sec. 7.5-7.6
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15
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Series solutions
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Sec. 7.7, 8.1
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16
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Sec. 8.2-8.4
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17
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(1/2 放假)
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18
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Final (1/9)
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